Cutoff-independence:
A crucial observation made in ref. [1]} was that the resulting scale associated with superconductivity is independent of the arbitrary choice of cutoff, \(\Lambda _0\) . Indeed, the only characteristic scale, namely the bandwidth \(W\)  determines the superconducting instability: \(T^{\vphantom{\dagger }}_{\rm c} \sim W \exp \big (-1\big /\alpha \rho ^2 U^2\big )\) , as alluded to earlier. While the details of the proof of cutoff independence can be found in ref. [1]}, we provide here some intuition for why this has to be the case. The main requirement for cutoff independence is that the Fermi liquid fixed point be the only nearby fixed point. This is certainly true in the weak-coupling limit.
